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A particle moves in the plane xy with co...

A particle moves in the plane xy with constant acceleration 'a' directed along the negative y-axis. The equation of motion of the particle has the form `y= px - qx^2` where p and q are positive constants. Find the velocity of the particle at the origin of co-ordinates.

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Taking X-axis horizontal and Y-axis vertical.
We have , `Y = Ax - Bx^(2)`
Comparing with equation of trajectory ,
`y = x tan alpha - (gx^(2))/(2u^(2) cos^(2) alpha)`
` = x tan alpha - (gx^(2))/(2u) (1+tan^(2) alpha)`
We have `A = tan alpha ` and `B = (g)/(2u^(2)) (1+A^(2))`
(or)` u^(2) = ((1+A)^(2)g)/(2B) (or) u = sqrt(((1+A)^(2)g)/(2B))`
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